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Deep reinforcement learning (DRL) has proven capable of superhuman performance on many complex tasks. To achieve this success, DRL algorithms train a decision-making agent to select the actions that maximize some long-term performance measure. In many consequential real-world domains, however, optimal performance is not enough to justify an algorithm’s use—for example, sometimes a system’s robustness, stability, or safety must be rigorously ensured. Thus, methods for verifying DRL systems have emerged. These algorithms can guarantee a system’s properties over an infinite set of inputs, but the task is not trivial. DRL relies on deep neural networks (DNNs). DNNs are often referred to as “black boxes” because examining their respective structures does not elucidate their decision-making processes. Moreover, the sequential nature of the problems DRL is used to solve promotes significant scalability challenges. Finally, because DRL environments are often stochastic, verification methods must account for probabilistic behavior. To address these complications, a new subfield has emerged. In this survey, we establish the foundations of DRL and DRL verification, define a taxonomy for DRL verification methods, describe approaches for dealing with stochasticity, characterize considerations related to writing specifications, enumerate common testing tasks/environments, and detail opportunities for future research.